In most cases where estimation with averaged data is performed,
interest lies on the parameters of a model at the individual level, but
grouped data are used because disaggregate data are not observed. In this
note we study the conditions under which it is possible to consistently
estimate the parameters of the individual data model using averaged data,
giving particular attention to the case of endogenous selection into
groups.We are grateful to an anonymous
referee for helpful comments and suggestions. We also thank Pedro Duarte
Neves, Les Godfrey, Paulo Parente, Maximiano Pinheiro, and Pedro Portugal
for helpful discussions. The usual disclaimer applies. Machado is
consultant for the Research Department of Banco de Portugal. Santos Silva
is grateful for the hospitality, working conditions, and financial support
provided by Banco de Portugal, which made this work possible. The authors
also gratefully acknowledge partial financial support from
Fundação para a Ciência e Tecnologia, program POCTI,
partially funded by FEDER.